Question: Calculate the product below and give your answer in scientific notation. $ {\left(8\times 10^{-3} \right) \times \left(0.0002 \right) =\ ?} $
Solution: First, let's change the second factor into scientific notation. $(8.0\times 10^{-3}) \times (0.0002) = (8.0\times 10^{-3}) \times (2.0\times 10^{-4}) $ Start by collecting the significands and exponents. $ ({8.0} \times {10^{-3}}) \times ({2.0} \times {10^{-4}}) = ({8.0} \times {2.0}) \times ({10^{-3}} \times {10^{-4}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {16.0} \times {10^{-3 \,+\, -4}}$ $= {16.0} \times {10^{-7}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${16.0}$ is the same as ${1.60 \times 10}$ or ${1.60 \times 10^{1}}$. $ = {1.60 \times 10^{1}} \times {10^{-7}} $ $ = 1.60 \times 10^{{1} + {-7}} $ $= 1.60\times 10^{-6}$